Nuprl Lemma : rminus-radd
∀[r,s:ℝ]. (-(r + s) = ((r(-1) * s) + (r(-1) * r)))
Proof
Definitions occuring in Statement :
req: x = y,
rmul: a * b,
rminus: -(x),
radd: a + b,
int-to-real: r(n),
real: ℝ,
uall: ∀[x:A]. B[x],
minus: -n,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
req_witness,
rminus_wf,
radd_wf,
rmul_wf,
int-to-real_wf,
real_wf,
radd_comm,
req_functionality,
rminus-as-rmul,
req_weakening,
rmul-distrib1
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
minusEquality,
natural_numberEquality,
independent_functionElimination,
sqequalRule,
isect_memberEquality,
because_Cache,
independent_isectElimination,
productElimination
Latex:
\mforall{}[r,s:\mBbbR{}]. (-(r + s) = ((r(-1) * s) + (r(-1) * r)))
Date html generated:
2016_05_18-AM-06_52_44
Last ObjectModification:
2015_12_28-AM-00_30_41
Theory : reals
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